At this point, a thought rang aloud in my mind: "why do all the primeval situations end up in a conflict?" I believe the answer in this story is: Senku was reasonably sure that he could beat Tsukasa and then achieve a better world than a compromise, and vice versa. Also, Tsukasa might have had less social priming towards cooperation.
As it happened, I recently watched all of Dr Stone too, and have mixed feelings about it but a lot of my observations are in the same vein.
I think you underplay the extremity of this: Tsukasa's problem is that Senku wins by default in this scenario. As soon as Senku revives a few dozen more people and reveals that the secret is nitric acid produced from bat guano (among many other possible sources), Tsukasa has basically lost. Even if he kills Senku then, there may well be a chemist or someone among the revived, who can easily replicate it. The revival of humanity means Tsukasa will soon be flooded by millions or billions of hostile intelligences; Tsukasa can then no more influence meaningfully the future of the world by punching all those millions of agents than he could in the original contemporary world where he was a successful MMA martial artist. He gets only one shot at controlling the future of humanity.
So a more realistic scenario than what actually happens for narrative shonen reasons, would be something like, Senku is revived after Tsukasa mistakenly thinks he's killed Senku, hikes a week or two away, finds one of Japan's myriad of caves/mountains and bat guano, starts reviving people, and a year later, Tsukasa's hunter-gatherers, venturing afield after a hard winter, discover that there's dozens of settlements of thousands of revived people who are busy reviving more. And then the modern world is irreversibly on the way to a reboot and there is nothing some teenagers dressed up like Fist of the North Star villains can do about it, because they can't revive many people themselves without defeating the whole point. (They'd either revive too few to matter, or wind up reviving their own worst enemies.) It is all-or-nothing. Eventually, even with narrative necessity and endless bad luck, Senku wins completely anyway; Tsukasa loses everything and has to settle for being bought off, in essence, because Senku manages to accumulate enough of a technological advantage even without any additional revivals. (The series unconvincingly says that Tsukasa's politics were superficial and so he got what he really wanted in the end, to try to rationalize how it worked out for him. Seems like cope to me!)
It is, in fact, remarkably similar to nuclear weapons or pandemics or even more so, AI, in terms of how unleashing a particular process almost immediately becomes irreversible, and so the phase immediately before the unleashing becomes all-important (even though it may look completely trivial, and looks like 2 highschoolers bickering over being a tankie and how awful a world with mortgages in it is, or some nerds arguing about speculative physics, or a lab tech sneezing in the street).
There is also an alternative realistic scenario where Tsukasa [temporarily?] wins. That happens if upon killing Senku, Tsukasa buries or destroys his body himself.
Though, to get a scientist not trying to undermine the empire, Tsukasa would need to play Newcomb-like Omega (conditioning reviving the scientist on him cooperating, as any other option qualifies as a ignorable threat). Not getting any science advances would put the tribe on the edge of loss (due to illnesses, Petrification Kingdom, inability to revive people fast enough, inability to anticipate outcomes of any specific revival order, etc).
Yes, while Tsukasa has no particular reason to think Senku could revive himself, he might have done that out of simple guilt/regret. Just one of many reasons that specific plan was very shonen-idiotic. (Your tolerance for Dr Stone's strange blend of oscillating rapidly between shonen-idiocy where everyone is holding idiot balls 24/7 in a world which makes zero sense, and Robinson Crusoe STEM nerd ratfic, will determine how much you enjoy it, I think.)
But even if Tsukasa accidentally deals with Senku in a definitive way, he still has the same basic issue: many people can defect and trigger a civilization-level reboot on their own, and he only has to screw up once. No matter how many 'statues' he destroys locally to prevent revival, and how carefully he selects who to revive, it just doesn't work statistically. (Even handwaving away the wildly absurd worldbuilding which postulates that there can be at least 2 stable villages of hundreds or thousands of humans living at an advanced tech level for 3000+ years without anyone ever recolonizing the rest of the world.) His preferred plan leaves way too much 'hardware overhang'; he needs a singleton, and it's not obvious where he'd ever get that.
(And the worldbuilding further implies that Tsukasa's plan is doomed because Senku is merely the first to wake up due to a double coincidence of location & his mental activity, and all the intact statues would revive eventually worldwide, and neither Tsukasa nor his successors could handle that.)
I really loved Dr Stone. It gave me the feeling that the science as magic sequences gave me. A deep appreciation for reality and the power it brings an individual to understand it deeply. I really hope to have more rationalists watch it in future.
I also recommend “Science fell in love, so I tried to prove it” for stats nerds. And “My Hero Academia” as the main character embodies “Tsuyoku Naritai!”
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Recently, I watched anime Dr Stone, and noticed that it was starting many thoughts like "why did social interactions turn out so?", "what might be the best way out of situation?" - in short, rationality-related. I really enjoyed watching with pauses to think for myself, and recommend it to all who are fine with anime.
In next three sections, I explain plot parts which felt especially inspiring to me, widening one's view on rationality - so, spoilers follow. Section "Wrapping up" deals with the whole show quality.
A reminder: this is fiction, not real-world evidence.
Premise
The protagonist, Senku Ishigami, is a "scientist" teen, excited to advance the world of technology. In particular, once he wanted to build a rocket; with some help and some years of exploring ideas, he achieved that dream, sending statuettes of his friends and himself to orbit.
Suddenly, birds began turning into stone. Senku noticed this phenomenon through social networks and, looking at reports from all over the world, managed to estimate the origin point of effect. Though, he wasn't able to discover any way to counteract the effect: very soon, the world was flooded with green energy, turning all humans into stone.
The teen noticed that he was still alive and began counting seconds to track the current season (as "waking up" in winter would be a probable death). And indeed, after a few thousand years the stone shell broke open, allowing Senku to start doing something. He also took care not to remove remaining pieces of stone, inferring that depetrification process involved some regeneration all around.
Interpretation
To this point, Senku has already 1) built a somewhat working rocket iterating over several possible designs, 2) discovered a petrification effect origin, 3) anticipated waking up and concentrated for survival. It should also be noted that he had a few friends who had fun with him but no girlfriends.
These behaviors align with acquiring knowledge (both from others' past observations and from actual world, highlighting both theoretical and empirical learning) and achieving goals, which are the points of epistemic and instrumental rationality respectively.
Stone World
In a stone world, Senku determined to revive all of humanity (which we only learn later) and restore technological civilization. He did some gathering and managed to start a campfire. (Note about anime accuracy: the teen could not start fire just rotating a branch with bare hands - as is often shown in cartoons - and had to use a tool instead, which seems more realistic). With help of his friend -- spuriously depetrified Taiju -- he discovered a way to wake up other statues conditional on them being intact.
A few months passed. With "miracle fluid" made, the teens went to depetrify their next friend Yuzuriha, only to be attacked by a few lions. (The story claims that this was the first attack, and that nor Senku nor Taiju had met lions in the area before.) Taiju, being reasonably strong, offered to hold the pride of lions off, sacrificing himself; Senku decided instead to revive a very strong person, Tsukasa Shishio, who was subsequently able to win the fight and vowed to protect all of them.
A few days later, Senku and Tsukasa discussed their goals and inferred that their ideas of best worlds clash, as Tsukasa wanted to build a "pure" world: not reviving those who don't do useful work in a wide sense, and not recreating dangerous technology like firearms (nor inventing even more powerful things).
The events continued with Tsukasa deciding to monopolize "miracle fluid" ingredients and to make Senku not restore technological civilization at all, possibly killing him to this end.
Reviewer's note
At this point, a thought rang aloud in my mind: "why do all the primeval situations end up in a conflict?" I believe the answer in this story is: Senku was reasonably sure that he could beat Tsukasa and then achieve a better world than a compromise, and vice versa. Also, Tsukasa might have had less social priming towards cooperation.
Still Stone World
Senku and his friends attempted to escape from Tsukasa. They didn't quite manage, so Senku "sacrificed" himself, being the main opponent to the other's goals; friends, left alone for a while and close to despair, finally found a piece of stone shell on Senku's body, which did regeneration and really revived him. Then, he left to find other people who were sending signals, recommending Taiju and Yuzuriha to become spies in Tsukasa's empire.
Interpretation
To this point, Senku has 1) remembered primitive tech and reconstructed some of it; 2) inferred Tsukasa's motives a bit before he said them out loud, then managed to withhold some information about his own capabilities; 3) remembered to distrust Tsukasa's protection vow (or just not took it seriously, which is a bit more probable considering power of terminal goals overriding whatever was said); 4) hidden his chance for a "second" life.
That's a good level of social interaction - both of obtaining information about others and of being convincing. Those are identical to the points of epistemic and instrumental rationality respectively.
Ishigami Village, up to end of the Stone War
From then, Senku concentrated on restoring technological advances, impressing other people from a village he met so that they joined him. He simultaneously cured a Very Important Person from village, won in a tournament (the second feat came pretty much randomly, though) and impressed others, so he became the village's chieftain.
There were a few battles against Tsukasa's Empire of Might, which primarily scared people but had zero casualties, with only one exception. Once, the battle stalled because of some fumes which were spreading along the ground; Hyoga (Tsukasa's right hand man) decided to check if those were toxic, and kicked two of his own soldiers there, indeed killing them (as the gas came from sulfuric acid spring).
Senku was not exploring any new tech during that, preferring instead to build what was possible. He with the villagers built a pair of cellphones and an armored car, which they used to take Empire of Might's base bloodlessly. A few threats to blow everything up were exchanged, but finally Tsukasa agreed to a ceasefire... Hyoga was not pleased with this outcome and stabbed his leader, but immediately got jailed, while Tsukasa was saved by cryopreservation.
Interpretation
In particular, these arcs demonstrate Senku's ideas: keep everyone alive whenever possible even if very hard, and make technology for the benefit of humanity.
As Senku doesn't attempt discovering new things, he does not count as a scientist in my opinion. Instead, he anticipates events, finds best items to solve problems, and can reach his goals (as shown in next seasons as well); in other words, he is a rationalist.
Wrapping up
Dr Stone has scenes-inlets describing some processes (both physical and chemical); some bloggers have verified those to be real (but somewhat simplified, including shorter taken time), matching claim of the anime itself "based on real concepts but fictional events". There are some implausible things, but I feel that probability decreases smoothly over watching anime - in contrast to some works, where some characters' actions can only be explained by authorial fiat.
Emotionally, the show didn't feel the slightest bit "dark", but instead was inspiring for me. It is based on becoming stronger and stronger. There are antagonists, but those avoid destroying everything of value; instead, conflicts are value-based.
The anime is not a good guide for either rationality or living in primitive society, I guess (after all, it is fiction!); however, it is a good reminder of what it means to be rational and grounded in reality. I recommend watching Dr Stone (or reading, as there's a manga version) to whoever doesn't find anime style repulsive.